Strong project management is increasingly recognised as essential to achieve impactful outcomes in externally-funded research projects hosted in Higher Education Institutes (HEIs). However, the characteristics of research project management, and how it differs from project management in other environments, have not been sufficiently explored. Key factors in research projects lead us to question the applicability of standard project management methodologies, and to explore optimum organisational approaches to project support. In this paper, from a practitioner perspective we consider the factors that influence forms of research project management and prior literature on the topic. We report on the results of a survey of project management modes and maturity undertaken among research project management professionals in EU, EEA and UK HEIs. Insights derived from the results provide a better understanding of how organisational research project management is currently implemented, and identify avenues for improvement, increasing fundamental understanding of this emerging professional domain.